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Year 2021, , 115 - 121, 30.06.2021
https://doi.org/10.47000/tjmcs.875446

Abstract

References

  • [1] Banas, J., Nalepa, R., On the space of functions with growths tempered by a modulus of continuity and its applications, J. Funct. Space Appl., (2013), 13 pages. doi:10.1155/2013/820437
  • [2] Berenguer, M.I., Munoz, M.V.F., Guillem, A.I.G., Galan, M.R., Numerical treatment of fixed point applied to the nonlinear Fredholm integral equation, Fixed Point Theory Appl., 2009(2009), 1–8.
  • [3] Caballero, J., Abdalla, M., Sadarangani, K., Solvability of a quadratic integral equation of fredholm type in H¨older spaces, Electron. J. Differ. Eq., 31(2014), 1–10.
  • [4] Caballero, M.J., Nalepa, R., Sadarangani, K., Solvability of a quadratic integral equation of Fredholm type with supremum in Hölder spaces, J. Funct. Space Appl., (2014).
  • [5] Fredholm, E.I., Sur une classe d’equations fonctionnelles, Acta Math., 27(1903), 365–390.
  • [6] Kirk, W.A., Srinavasan, P.S., Veeramani, P., Fixed Points for mapping satisfying cyclical contractive conditions, Fixed Point Theory, 4(2003), 79–89.
  • [7] Pathak, H.K., Khan, M.S., Tiwari, R., A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl. Arch., 53(2007), 961–71.
  • [8] Rasham, T., Shoaib, A., Hussain, N., Arshad, M., Khan, S.U., Common fixed point results for new Ciric-type rational multivalued F-contraction with an application, J. Fixed Point Theory Appl., 20(1)(2018), 1–16.
  • [9] Rus, M.D., A note on the existaence of positive solution of Fredholm integral equations, Fixed Point Theory, 5(2004), 369–377.
  • [10] Schauder, J., Der Fixpunktsatz in Funktionalriiumen, Studia Math., 2(1930), 171–180.

An Application to the Existence of Solutions of the Integral Equations

Year 2021, , 115 - 121, 30.06.2021
https://doi.org/10.47000/tjmcs.875446

Abstract

Integral equations provide mathematical models of many important problems in the physical sciences and engineering. This paper treats one class of such equations, concentrating on methods involving the use of classical fixed point theorem. The study of integral equations in connection with nonlinear equations has a long history, during which a variety of approaches has emerged. Here, we effectively use a strategy that derives key properties of the solvability of integral equations from previously established results in Hölder spaces. Moreover, our approach leads to solvability of the Fredholm integral equations.

References

  • [1] Banas, J., Nalepa, R., On the space of functions with growths tempered by a modulus of continuity and its applications, J. Funct. Space Appl., (2013), 13 pages. doi:10.1155/2013/820437
  • [2] Berenguer, M.I., Munoz, M.V.F., Guillem, A.I.G., Galan, M.R., Numerical treatment of fixed point applied to the nonlinear Fredholm integral equation, Fixed Point Theory Appl., 2009(2009), 1–8.
  • [3] Caballero, J., Abdalla, M., Sadarangani, K., Solvability of a quadratic integral equation of fredholm type in H¨older spaces, Electron. J. Differ. Eq., 31(2014), 1–10.
  • [4] Caballero, M.J., Nalepa, R., Sadarangani, K., Solvability of a quadratic integral equation of Fredholm type with supremum in Hölder spaces, J. Funct. Space Appl., (2014).
  • [5] Fredholm, E.I., Sur une classe d’equations fonctionnelles, Acta Math., 27(1903), 365–390.
  • [6] Kirk, W.A., Srinavasan, P.S., Veeramani, P., Fixed Points for mapping satisfying cyclical contractive conditions, Fixed Point Theory, 4(2003), 79–89.
  • [7] Pathak, H.K., Khan, M.S., Tiwari, R., A common fixed point theorem and its application to nonlinear integral equations, Comput. Math. Appl. Arch., 53(2007), 961–71.
  • [8] Rasham, T., Shoaib, A., Hussain, N., Arshad, M., Khan, S.U., Common fixed point results for new Ciric-type rational multivalued F-contraction with an application, J. Fixed Point Theory Appl., 20(1)(2018), 1–16.
  • [9] Rus, M.D., A note on the existaence of positive solution of Fredholm integral equations, Fixed Point Theory, 5(2004), 369–377.
  • [10] Schauder, J., Der Fixpunktsatz in Funktionalriiumen, Studia Math., 2(1930), 171–180.
There are 10 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Merve Temizer Ersoy 0000-0003-4364-9144

Publication Date June 30, 2021
Published in Issue Year 2021

Cite

APA Temizer Ersoy, M. (2021). An Application to the Existence of Solutions of the Integral Equations. Turkish Journal of Mathematics and Computer Science, 13(1), 115-121. https://doi.org/10.47000/tjmcs.875446
AMA Temizer Ersoy M. An Application to the Existence of Solutions of the Integral Equations. TJMCS. June 2021;13(1):115-121. doi:10.47000/tjmcs.875446
Chicago Temizer Ersoy, Merve. “An Application to the Existence of Solutions of the Integral Equations”. Turkish Journal of Mathematics and Computer Science 13, no. 1 (June 2021): 115-21. https://doi.org/10.47000/tjmcs.875446.
EndNote Temizer Ersoy M (June 1, 2021) An Application to the Existence of Solutions of the Integral Equations. Turkish Journal of Mathematics and Computer Science 13 1 115–121.
IEEE M. Temizer Ersoy, “An Application to the Existence of Solutions of the Integral Equations”, TJMCS, vol. 13, no. 1, pp. 115–121, 2021, doi: 10.47000/tjmcs.875446.
ISNAD Temizer Ersoy, Merve. “An Application to the Existence of Solutions of the Integral Equations”. Turkish Journal of Mathematics and Computer Science 13/1 (June 2021), 115-121. https://doi.org/10.47000/tjmcs.875446.
JAMA Temizer Ersoy M. An Application to the Existence of Solutions of the Integral Equations. TJMCS. 2021;13:115–121.
MLA Temizer Ersoy, Merve. “An Application to the Existence of Solutions of the Integral Equations”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 1, 2021, pp. 115-21, doi:10.47000/tjmcs.875446.
Vancouver Temizer Ersoy M. An Application to the Existence of Solutions of the Integral Equations. TJMCS. 2021;13(1):115-21.